Eagle Nest is a village in Colfax County, New Mexico. The population was 290 at the time of the 2010 census. Located along the Enchanted Circle Scenic Byway, Eagle Nest is a small summer-home and resort destination. Originally named Therma, the village was renamed Eagle Nest in the 1930s. The town is located in the Sangre de Cristo Mountains in nort…Eagle Nest is a village in Colfax County, New Mexico. The population was 290 at the time of the 2010 census. Located along the Enchanted Circle Scenic Byway, Eagle Nest is a small summer-home and resort destination. Originally named Therma, the village was renamed Eagle Nest in the 1930s. The town is located in the Sangre de Cristo Mountains in northern New Mexico near the Colorado border.